JEE Questions for Maths Mathematical Logic And Boolean Algebra Quiz 2 - MCQExams.com

Consider the switching circuit given below
Maths-Mathematical Logic and Boolean Algebra-38006.png
  • a' ∙ b' ∙c
  • a + b + c'
  • a∙b∙c'
  • a' + b' + c
Let B be a boolean algebra. If x, y ϵ B, then (x∙y)' is equal to
  • x ∙ y
  • x ∙ y'
  • x' ∙ y'
  • (x' - y')
  • x' + y'
The dual of x + (y ∙ x) = x is
  • (x + y) ∙ (x + x) = x
  • x ∙ (y + x) = x
  • x ∙ (y ∙ x) = x
  • None of these
Dual of (x + y) ∙ (x += x + x ∙y + y is
  • (x ∙ y) + (x ∙= x ∙ (x + y) ∙ y
  • (x + y) + (x ∙= x ∙ (x + y) ∙ y
  • (x ∙ y)(x ∙= x ∙(x + y) ∙ y
  • None of the above
In boolean algebra, the unit element ' 1'
  • has two values
  • is unique
  • has atleast two values
  • None of these
If flow values of switches x1, x2 and x3 are respectively 0. 0 and 1, then the flow value of the circuit
S = (x1 ' ∙ x2' ∙ x3) +(x 1 ∙ x2' ∙ x3') + (x1'∙ x2' ∙ x3')
  • 0
  • 1
  • 2
  • None of these
The Statement ~ (p ↔ ~ q) is
  • equivalent to p ↔ q
  • equivalent to ~ p ↔ q
  • a tautology
  • a fallacy

Maths-Mathematical Logic and Boolean Algebra-38007.png

  • Maths-Mathematical Logic and Boolean Algebra-38008.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38009.png

  • Maths-Mathematical Logic and Boolean Algebra-38010.png

  • Maths-Mathematical Logic and Boolean Algebra-38011.png

Maths-Mathematical Logic and Boolean Algebra-38012.png
  • tautology
  • contradiction
  • Neither (a) nor (b)
  • None of these
If p, q and r are any three logical statements, then which one of the following is correct?

  • Maths-Mathematical Logic and Boolean Algebra-38013.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38014.png

  • Maths-Mathematical Logic and Boolean Algebra-38015.png

  • Maths-Mathematical Logic and Boolean Algebra-38016.png

  • Maths-Mathematical Logic and Boolean Algebra-38017.png

Maths-Mathematical Logic and Boolean Algebra-38018.png
  • F, T, F
  • F, F, F
  • T, T, T
  • T, F, F
  • F, F, T

Maths-Mathematical Logic and Boolean Algebra-38019.png

  • Maths-Mathematical Logic and Boolean Algebra-38020.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38021.png

  • Maths-Mathematical Logic and Boolean Algebra-38022.png

  • Maths-Mathematical Logic and Boolean Algebra-38023.png

  • Maths-Mathematical Logic and Boolean Algebra-38024.png

Maths-Mathematical Logic and Boolean Algebra-38025.png
  • Statemenl. I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
  • Statement I is correct; Statement II is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct

Maths-Mathematical Logic and Boolean Algebra-38026.png

  • Maths-Mathematical Logic and Boolean Algebra-38027.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38028.png

  • Maths-Mathematical Logic and Boolean Algebra-38029.png

  • Maths-Mathematical Logic and Boolean Algebra-38030.png
  • None of these
Consider the following statements
p: Suman is brilliant.
g: Suman is rich.
r: Suman is honest.
The negation of the statement 'Suman is brilliant and dishonest if and only if Suman is rich' can be expressed as

  • Maths-Mathematical Logic and Boolean Algebra-38031.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38032.png

  • Maths-Mathematical Logic and Boolean Algebra-38033.png

  • Maths-Mathematical Logic and Boolean Algebra-38034.png
The only statement among the following which is a tautology, is

  • Maths-Mathematical Logic and Boolean Algebra-38035.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38036.png

  • Maths-Mathematical Logic and Boolean Algebra-38037.png

  • Maths-Mathematical Logic and Boolean Algebra-38038.png

Maths-Mathematical Logic and Boolean Algebra-38039.png

  • Maths-Mathematical Logic and Boolean Algebra-38040.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38041.png

  • Maths-Mathematical Logic and Boolean Algebra-38042.png

  • Maths-Mathematical Logic and Boolean Algebra-38043.png

Maths-Mathematical Logic and Boolean Algebra-38044.png
  • roses are not red and the Sun is not a star
  • it is not true that roses are red or the Sun is not a star
  • it is not true that roses are red and the Sun is a star
  • roses are not red or the Sun is a star
  • it is not true that roses are red and the Sun is a star
Which of the following is not a logical statement?
  • 8 is less than 6
  • Every set is a finite set
  • Kashmir is far from here
  • The Sun is a star

Maths-Mathematical Logic and Boolean Algebra-38045.png

  • Maths-Mathematical Logic and Boolean Algebra-38046.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38047.png

  • Maths-Mathematical Logic and Boolean Algebra-38048.png
  • None of these

Maths-Mathematical Logic and Boolean Algebra-38049.png
  • p
  • ~p
  • q
  • ~q

Maths-Mathematical Logic and Boolean Algebra-38050.png

  • Maths-Mathematical Logic and Boolean Algebra-38051.png
  • 2)
    Maths-Mathematical Logic and Boolean Algebra-38052.png

  • Maths-Mathematical Logic and Boolean Algebra-38053.png

  • Maths-Mathematical Logic and Boolean Algebra-38054.png

  • Maths-Mathematical Logic and Boolean Algebra-38055.png
If p : 7 is not greater than 4 and q : Paris is in France, are two statements. Then, ~ (p ⋁ q) is the statement
  • 7 is greater than 4 or Paris is not in France
  • 7 is not greater than 4 and Paris is not in France
  • 7 is greater than 4 and Paris is in France
  • 7 is not greater than 4 or Paris is not in France
  • 7 is greater than 4 and Paris is not in France
Consider the following statements
Statement I ~(p ↔ q) is equivalent to p ↔ q.
Statement II ~ (p ↔ q) is a tautology.
  • Statement I is correct, Statement II is correct; Statement 11 is a correct explanation for Statement I
  • Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct
~ ( ~ p → q) is equivalent to
  • p ⋀ ~ q
  • ~ p ⋀ q
  • ~ p ⋀ ~ q
  • ~ p ⋁ ~ q
Simplify (p ⋁ q) ⋀ (p ⋁ ~ q).
  • P
  • T
  • F
  • q
The negation of p ⋀ (q → ~ q) is
  • ~ p ⋀ (q ⋀ r)
  • p ⋁ (q ⋁ r)
  • p ⋁ (q ⋀ r)
  • ~ p ⋁ (q ⋀ r)
Identify the incorrect statement.
  • ~ [p ⋁ (~ q)] ≡ ( ~ p) ⋀ q
  • [p ⋁ q] ⋁ (~ p) is a tautology
  • [p ⋀ q] ⋀ (~ p) is a contradiction
  • ~ [p ⋀ (~ p)] is a tautology
  • ~ (p ⋁ q) ≡ (~ p) ⋁ (~ q)
The statement p → (q → p) is equivalent to
  • p → (p ↔ q)
  • p → (p → q)
  • p → (p ⋁ q)
  • p → (p ⋀ q)
If p: 4 is an even prime number, q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2, then which one of the following is correct?
  • (p ⋀ q)
  • (p ⋁ q) ⋀ ~ r
  • ~ (q ⋀ r) ⋁ p
  • ~ p ⋁ (q ⋀ r)
  • p ↔ (q ⋀ r)
0:0:1


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